Convert 101 101 111 001 193 to a Signed Binary in One's (1's) Complement Representation

How to convert decimal number 101 101 111 001 193(10) to a signed binary in one's (1's) complement representation

What are the steps to convert decimal number
101 101 111 001 193 to a signed binary in one's (1's) complement representation?

  • A signed integer, written in base ten, or a decimal system number, is a number written using the digits 0 through 9 and the sign, which can be positive (+) or negative (-). If positive, the sign is usually not written. A number written in base two, or binary, is a number written using only the digits 0 and 1.

1. Divide the number repeatedly by 2:

Keep track of each remainder.

Stop when you get a quotient that is equal to zero.


  • division = quotient + remainder;
  • 101 101 111 001 193 ÷ 2 = 50 550 555 500 596 + 1;
  • 50 550 555 500 596 ÷ 2 = 25 275 277 750 298 + 0;
  • 25 275 277 750 298 ÷ 2 = 12 637 638 875 149 + 0;
  • 12 637 638 875 149 ÷ 2 = 6 318 819 437 574 + 1;
  • 6 318 819 437 574 ÷ 2 = 3 159 409 718 787 + 0;
  • 3 159 409 718 787 ÷ 2 = 1 579 704 859 393 + 1;
  • 1 579 704 859 393 ÷ 2 = 789 852 429 696 + 1;
  • 789 852 429 696 ÷ 2 = 394 926 214 848 + 0;
  • 394 926 214 848 ÷ 2 = 197 463 107 424 + 0;
  • 197 463 107 424 ÷ 2 = 98 731 553 712 + 0;
  • 98 731 553 712 ÷ 2 = 49 365 776 856 + 0;
  • 49 365 776 856 ÷ 2 = 24 682 888 428 + 0;
  • 24 682 888 428 ÷ 2 = 12 341 444 214 + 0;
  • 12 341 444 214 ÷ 2 = 6 170 722 107 + 0;
  • 6 170 722 107 ÷ 2 = 3 085 361 053 + 1;
  • 3 085 361 053 ÷ 2 = 1 542 680 526 + 1;
  • 1 542 680 526 ÷ 2 = 771 340 263 + 0;
  • 771 340 263 ÷ 2 = 385 670 131 + 1;
  • 385 670 131 ÷ 2 = 192 835 065 + 1;
  • 192 835 065 ÷ 2 = 96 417 532 + 1;
  • 96 417 532 ÷ 2 = 48 208 766 + 0;
  • 48 208 766 ÷ 2 = 24 104 383 + 0;
  • 24 104 383 ÷ 2 = 12 052 191 + 1;
  • 12 052 191 ÷ 2 = 6 026 095 + 1;
  • 6 026 095 ÷ 2 = 3 013 047 + 1;
  • 3 013 047 ÷ 2 = 1 506 523 + 1;
  • 1 506 523 ÷ 2 = 753 261 + 1;
  • 753 261 ÷ 2 = 376 630 + 1;
  • 376 630 ÷ 2 = 188 315 + 0;
  • 188 315 ÷ 2 = 94 157 + 1;
  • 94 157 ÷ 2 = 47 078 + 1;
  • 47 078 ÷ 2 = 23 539 + 0;
  • 23 539 ÷ 2 = 11 769 + 1;
  • 11 769 ÷ 2 = 5 884 + 1;
  • 5 884 ÷ 2 = 2 942 + 0;
  • 2 942 ÷ 2 = 1 471 + 0;
  • 1 471 ÷ 2 = 735 + 1;
  • 735 ÷ 2 = 367 + 1;
  • 367 ÷ 2 = 183 + 1;
  • 183 ÷ 2 = 91 + 1;
  • 91 ÷ 2 = 45 + 1;
  • 45 ÷ 2 = 22 + 1;
  • 22 ÷ 2 = 11 + 0;
  • 11 ÷ 2 = 5 + 1;
  • 5 ÷ 2 = 2 + 1;
  • 2 ÷ 2 = 1 + 0;
  • 1 ÷ 2 = 0 + 1;

2. Construct the base 2 representation of the positive number:

Take all the remainders starting from the bottom of the list constructed above.

101 101 111 001 193(10) = 101 1011 1111 0011 0110 1111 1100 1110 1100 0000 0110 1001(2)

3. Determine the signed binary number bit length:

  • The base 2 number's actual length, in bits: 47.

  • A signed binary's bit length must be equal to a power of 2, as of:
  • 21 = 2; 22 = 4; 23 = 8; 24 = 16; 25 = 32; 26 = 64; ...
  • The first bit (the leftmost) indicates the sign:
  • 0 = positive integer number, 1 = negative integer number

The least number that is:

1) a power of 2

2) and is larger than the actual length, 47,

3) so that the first bit (leftmost) could be zero
(we deal with a positive number at this moment)

=== is: 64.


4. Get the positive binary computer representation on 64 bits (8 Bytes):

If needed, add extra 0s in front (to the left) of the base 2 number, up to the required length, 64.


Decimal Number 101 101 111 001 193(10) converted to signed binary in one's complement representation:

101 101 111 001 193(10) = 0000 0000 0000 0000 0101 1011 1111 0011 0110 1111 1100 1110 1100 0000 0110 1001

Spaces were used to group digits: for binary, by 4, for decimal, by 3.

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How to convert signed integers from the decimal system to signed binary in one's complement representation

Follow the steps below to convert a signed base 10 integer number to signed binary in one's complement representation:

  • 1. If the number to be converted is negative, start with the positive version of the number.
  • 2. Divide repeatedly by 2 the positive representation of the integer number that is to be converted to binary, keeping track of each remainder, until we get a quotient that is equal to ZERO.
  • 3. Construct the base 2 representation of the positive number, by taking all the remainders starting from the bottom of the list constructed above. Thus, the last remainder of the divisions becomes the first symbol (the leftmost) of the base two number, while the first remainder becomes the last symbol (the rightmost).
  • 4. Binary numbers represented in computer language must have 4, 8, 16, 32, 64, ... bit length (a power of 2) - if needed, fill in '0' bits in front (to the left) of the base 2 number calculated above, up to the right length; this way the first bit (leftmost) will always be '0', correctly representing a positive number.
  • 5. To get the negative integer number representation in signed binary one's complement, replace all '0' bits with '1's and all '1' bits with '0's.

Example: convert the negative number -49 from the decimal system (base ten) to signed binary one's complement:

  • 1. Start with the positive version of the number: |-49| = 49
  • 2. Divide repeatedly 49 by 2, keeping track of each remainder:
    • division = quotient + remainder
    • 49 ÷ 2 = 24 + 1
    • 24 ÷ 2 = 12 + 0
    • 12 ÷ 2 = 6 + 0
    • 6 ÷ 2 = 3 + 0
    • 3 ÷ 2 = 1 + 1
    • 1 ÷ 2 = 0 + 1
  • 3. Construct the base 2 representation of the positive number, by taking all the remainders starting from the bottom of the list constructed above:
    49(10) = 11 0001(2)
  • 4. The actual bit length of base 2 representation is 6, so the positive binary computer representation of a signed binary will take in this case 8 bits (the least power of 2 that is larger than 6) - add '0's in front of the base 2 number, up to the required length:
    49(10) = 0011 0001(2)
  • 5. To get the negative integer number representation in signed binary one's complement, replace all '0' bits with '1's and all '1' bits with '0's:
    -49(10) = 1100 1110
  • Number -49(10), signed integer, converted from the decimal system (base 10) to signed binary in one's complement representation = 1100 1110